人类财富演变：趋势和波动
Human wealth evolution: trends and fluctuations
摘要：
对人类财富历史的因果描述是可以想象的吗？为了研究这一问题，我们引入了一个简单的因果关系，虽然强聚合模型，假设观察到的财富增长主要是由人类的合作努力，其强度本身增加的财富增加。作为实证参考，我们使用时间序列描述八个世纪的人均年国内生产总值（GDP）的三个欧洲国家，英国，法国和瑞典。该模型需要足够大的人口来应对破坏性事件，例如饥荒、流行病和战争，而不是破坏社会的基本运作。财富演化趋势可以用一个含三个自由参数的常微分方程来描述。该解决方案具有有限时间奇点，这表明缺乏长期可持续性。奇点发生的年份在公元2020年附近从一个国家到另一个国家略有变化。1900年后缩减的GDP时间序列产生了类似的奇点发生值，因此可以在一百多年前预测。缩减从早期到公元1700年的GDP序列也产生了对奇点时间的稳定和一致的预测。{功率谱是针对跨越八个世纪的去趋势数据以及同一时期的第一个和最后四个世纪获得的。所有频谱都有一个总的特征，其中功率随着频率的平方而衰减。嵌入的峰值让人想起经济文献中描述的周期，但也存在于工业化之前的时间序列中。国内生产总值数列的背景波动，初步解释为社会对破坏性随机事件的反应。例如，划时代的发现之后的新经济活动，以及战争和流行病
英文摘要：
Is a causal description of human wealth history conceivable? To investigate the matter we introduce a simple causal albeit strongly aggregated model, assuming that the observed wealth growth is mainly driven by human collaborative efforts whose intensity itself increases with increasing wealth. As an empirical reference we use time series describing eight centuries of per capita annual gross domestic products (GDP) of three European countries, the UK, France and Sweden. The model requires a population large enough for disruptive events, e.g. famine, epidemics and wars, not to destroy the fundamental workings of society. The wealth evolution trend can then be described by an ordinary differential equation with three free parameters. The solution features a finite time singularity, which suggests a lack of long term sustainability. The year at which the singularity occurs has a slight variation near 2020 AD from one country to another. GDP time series curtailed after 1900 AD produce similar values for the occurrence of the singularity, which thus could be predicted more than hundred years ago. Curtailing the GDP series from the early years up to 1700 AD also produces stable and consistent predictions for the singularity time. {Power spectra are obtained for de-trended data spanning eight centuries, as well as for the first and last four centuries of the same period. All spectra have an overall signature where the power decays as the inverse frequency squared. The embedded peaks are reminiscent of the cycles described in the economic literature, but are also present in time series far predating industrialization. The background fluctuations in the GDP series is tentatively interpreted as societal response to disruptive stochastic events. e.g. new economic activities following epochal discoveries, as well as wars and epidemics
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
